Fluid properties are the foundation of aerodynamics. Understanding density, pressure, viscosity, and compressibility is crucial for analyzing how air behaves around aircraft. These properties determine how fluids flow, exert forces, and respond to changes in their environment.

This knowledge forms the basis for more complex aerodynamic concepts. By grasping these fundamental properties, you'll be better equipped to tackle advanced topics like lift, drag, and boundary layer theory in aircraft design and performance analysis.

Density and specific gravity

• Density is a fundamental property of fluids that describes the mass per unit volume of a substance
• Specific gravity compares the density of a fluid to a reference fluid (water for liquids, air for gases) at a specified temperature
• Understanding density and specific gravity is crucial in aerodynamics for determining the behavior of fluids, such as air, in various flow conditions

Pressure in static fluids

Absolute vs gauge pressure

• Absolute pressure measures the total pressure exerted by a fluid, including atmospheric pressure
• Gauge pressure measures the pressure relative to the local atmospheric pressure
• In aerodynamics, both absolute and gauge pressures are used depending on the specific application and reference frame

Hydrostatic pressure variation

• Hydrostatic pressure is the pressure exerted by a fluid at rest due to its weight
• Pressure in a static fluid increases linearly with depth, following the equation $p = \rho gh$, where $p$ is pressure, $\rho$ is fluid density, $g$ is acceleration due to gravity, and $h$ is the depth below the surface
• Hydrostatic pressure variation is important in understanding the forces acting on submerged objects and the stability of floating bodies

Viscosity of fluids

Dynamic vs kinematic viscosity

• Dynamic viscosity, also known as absolute viscosity, is a measure of a fluid's resistance to shear stress and is expressed in units of $Pa \cdot s$ (pascal-seconds)
• Kinematic viscosity is the ratio of dynamic viscosity to fluid density and is expressed in units of $m^2/s$ (square meters per second)
• In aerodynamics, both dynamic and kinematic viscosities are used to characterize the flow behavior and resistance to deformation in fluids

Newtonian vs non-Newtonian fluids

• Newtonian fluids exhibit a linear relationship between shear stress and strain rate, with a constant viscosity independent of the applied shear stress (examples: air, water)
• Non-Newtonian fluids have a viscosity that varies with the applied shear stress or strain rate (examples: blood, paint)
• Most fluids encountered in aerodynamics, such as air, are considered Newtonian fluids under normal conditions

Compressibility of fluids

Bulk modulus of elasticity

• The bulk modulus of elasticity, denoted by $K$, is a measure of a fluid's resistance to uniform compression
• It is defined as the ratio of the change in pressure to the fractional change in volume, expressed as $K = -V \frac{dp}{dV}$, where $V$ is the initial volume, $dp$ is the change in pressure, and $dV$ is the change in volume
• The compressibility of fluids is an important consideration in high-speed aerodynamics, where significant pressure changes can occur

Speed of sound

• The speed of sound, denoted by $c$, is the speed at which pressure waves propagate through a fluid medium
• It is related to the bulk modulus of elasticity and fluid density by the equation $c = \sqrt{\frac{K}{\rho}}$, where $K$ is the bulk modulus and $\rho$ is the fluid density
• The speed of sound is a critical parameter in aerodynamics, as it determines the behavior of fluids in compressible flow regimes (examples: supersonic and hypersonic flows)

Surface tension and capillary effects

• Surface tension is a property of fluids that arises from the cohesive forces between molecules at the surface
• It is responsible for the formation of droplets, bubbles, and menisci, and plays a role in capillary action, where fluids rise or fall in narrow spaces (examples: water in a glass tube, ink in a pen)
• While surface tension and capillary effects are less significant in large-scale aerodynamic flows, they can be important in micro-scale fluid systems and in understanding the behavior of liquid fuels

Fluid statics

Buoyancy and Archimedes' principle

• Buoyancy is the upward force exerted by a fluid on an object immersed in it, due to the pressure difference between the top and bottom of the object
• Archimedes' principle states that the buoyant force acting on an object is equal to the weight of the fluid displaced by the object
• Buoyancy and Archimedes' principle are important in understanding the stability and behavior of objects submerged in fluids, such as aircraft fuel tanks and floating structures

Hydrostatic force on submerged surfaces

• Hydrostatic force is the force exerted by a fluid at rest on a submerged surface due to the pressure distribution
• The magnitude of the hydrostatic force depends on the fluid density, the surface area, and the depth of the centroid of the surface below the fluid surface
• Calculating hydrostatic forces is crucial in designing aircraft components that interact with fluids, such as control surfaces and fuel tanks

Ideal fluid concept

Inviscid flow assumption

• An inviscid fluid is a hypothetical fluid with zero viscosity, meaning it offers no resistance to shear stress
• The inviscid flow assumption simplifies the analysis of fluid flow by neglecting the effects of viscosity, which is a reasonable approximation for high-Reynolds-number flows away from solid boundaries
• In aerodynamics, the inviscid flow assumption is often used in preliminary design and analysis, such as in potential flow theory and thin airfoil theory

Irrotational flow condition

• Irrotational flow is a type of fluid flow in which the fluid particles do not rotate about their own axes
• Mathematically, the irrotational flow condition is expressed as $\nabla \times \vec{V} = 0$, where $\vec{V}$ is the velocity vector field and $\nabla \times$ is the curl operator
• Irrotational flow is a common assumption in potential flow theory and simplifies the analysis of fluid flow in many aerodynamic applications

Fluid kinematics

Streamlines and pathlines

• Streamlines are curves that are everywhere tangent to the velocity vector field at a given instant in time
• Pathlines are the actual paths followed by individual fluid particles over time
• In steady flow, streamlines and pathlines coincide, while in unsteady flow, they may differ
• Understanding streamlines and pathlines is essential for visualizing and analyzing fluid flow patterns in aerodynamics

Steady vs unsteady flow

• Steady flow is a type of fluid flow in which the flow properties (velocity, pressure, density) at any point do not change with time
• Unsteady flow, also known as non-steady or transient flow, is a type of fluid flow in which the flow properties vary with time
• Many aerodynamic problems can be approximated as steady flow for simplicity, but unsteady flow analysis is necessary for capturing time-dependent phenomena (examples: turbulence, vortex shedding)

Laminar vs turbulent flow

• Laminar flow is a type of fluid flow characterized by smooth, parallel layers of fluid with no mixing between the layers
• Turbulent flow is a type of fluid flow characterized by chaotic and irregular motion, with mixing between fluid layers
• The transition from laminar to turbulent flow depends on the Reynolds number, which is a dimensionless quantity that relates the inertial forces to the viscous forces in a fluid
• Understanding the differences between laminar and turbulent flow is crucial in aerodynamics, as it affects drag, heat transfer, and mixing processes

Fluid dynamics

Conservation of mass

• The conservation of mass principle states that mass cannot be created or destroyed in a closed system
• For fluid flow, this principle is expressed by the continuity equation, which relates the time rate of change of fluid density to the divergence of the mass flux
• In aerodynamics, the conservation of mass is a fundamental principle used in deriving the governing equations of fluid motion

Conservation of momentum

• The conservation of momentum principle states that the total momentum of a closed system remains constant in the absence of external forces
• For fluid flow, this principle is expressed by the Navier-Stokes equations, which relate the time rate of change of fluid momentum to the forces acting on the fluid (pressure, viscous, and body forces)
• The conservation of momentum is a key principle in aerodynamics, used in analyzing the forces acting on aircraft and predicting their motion

Conservation of energy

• The conservation of energy principle states that energy cannot be created or destroyed, only converted from one form to another
• For fluid flow, this principle is expressed by the energy equation, which relates the time rate of change of fluid energy to the work done by the fluid and the heat transfer
• In aerodynamics, the conservation of energy is important in analyzing the performance of aircraft engines, heat exchangers, and other thermal systems